Wireless communications systems are used in a variety of telecommunications systems, television, radio and other media systems, data communication networks, and other systems to convey information between remote points using wireless transmitters and wireless receivers. A transmitter is an electronic device which, usually with the aid of an antenna, propagates an electromagnetic signal such as radio, television, or other telecommunications. Transmitters often include signal amplifiers which receive a radio-frequency or other signal, amplify the signal by a predetermined gain, and communicate the amplified signal. On the other hand, a receiver is an electronic device which, also usually with the aid of an antenna, receives and processes a wireless electromagnetic signal. In certain instances, a transmitter and receiver may be combined into a single device called a transceiver.
Transmitters, receivers, and transceivers often include components known as oscillators. An oscillator may serve many functions in a transmitter, receiver, and/or transceiver, including generating local oscillator signal (usually in a radio-frequency range) for upconverting baseband signals onto a radio-frequency (RF) carrier and performing modulation for transmission of signals, and/or for downconverting RF signals to baseband signals and performing demodulation of received signals.
To achieve desired functionality, such oscillators must often have designs that produce precise operating characteristics. For example, it is often critical that oscillator circuits operate independently of the temperature of the oscillator circuit. However, in many existing oscillator circuits, variations in temperature may lead to undesired variations in the frequency of oscillation of an oscillator circuit. Such variations over temperature may result from various factors, including temperature dependence of a resonator used to create an oscillation frequency.
As is known in the art, the frequency response of a crystal resonator as a function if temperature may be approximated by the following equation:f(T)=f0+a1(T−T0)+a2(T−T0)2+a3(T−T0)3 where:
T is the temperature,
f(T) is the resonant frequency of the resonator at temperature T, and
f0 is the resonant frequency of the crystal at temperature T0.
As is also known, the coefficients a1, a2, and a3 of the above equation may vary such that each resonator must be separately characterized to determine its frequency versus temperature response.
In addition to the polynomial equation set forth above, a lot of crystal resonators may be characterized over a series of temperatures to determine their frequency versus temperature responses, such data may be stored in a lookup table or other data structure. As a result, a typical frequency versus temperature response may be determined by reference to the lookup table.
Designers of oscillator circuits often include compensation circuitry in order to minimize the temperature dependence of resonators in an effort to maintain an approximately constant output frequency over a given temperature range. Initially, during manufacturing a compensation circuit would be manually adjusted based upon grading or characterization of the resonator. Such approach was prone to human error and time consuming. To overcome the shortcomings of the practice of manual adjustment of compensation circuits based on grading, an approach was developed whereby a temperature sensing circuit of an oscillator would determine temperature and, based on such temperature, a compensation circuit of the oscillator would vary the capacitance of a variable capacitor coupled to a resonator, this inducing a frequency change in the oscillator circuit compensating for the frequency change of the resonator due to temperature. Such temperature based compensation was often determined by characterizing a random sample of resonators to determine a typical or average temperature dependence characteristic for a lot of crystals.
However, such approaches did not adequately compensate for process variations among resonators. For example, as is known in the art, a resonator may be statistically modeled as a resistor, inductor, and two capacitors, as shown in FIG. 5. Due to process variations during manufacture, the properties of such modeled electrical elements (e.g., resistance, inductance, and capacitance) may vary from one resonator to the next. Due to such variations, the temperature dependence functions of each resonator in a lot may vary from one another, thus reducing the effectiveness of applying an averaged temperature characteristic as a means of temperature compensation. That is, referencing the equation above, each resonator may have varying values of f0, T0, a1, a2, and/or a3, or may deviate from lookup table entries characterizing the expected frequency versus temperature characteristics of a lot of resonators. Thus, using traditional approaches, in order to adequately account for such process variations in resonators, time-consuming and error-prone grading of crystals may be required.